A Polygonal Finite Element Method for Stokes Equations

In this paper, we extend the Bernardi-Raugel element [1] to convex polygonal meshes by using generalized barycentric coordinates. Comparing traditional discretizations defined on triangular and rectangular meshes, can be more flexible when dealing with complicated domains or curved boundaries. Theoretical analysis of new follows standard mixed finite theory for Stokes equations, i.e., shall prove discrete inf-sup condition (LBB condition) constructing a Fortin operator. Because there is no scaling argument coordinates are in general not polynomials, special treatments required analysis. We that extended has optimal convergence rates. Supporting numerical results also presented.